INFERENCE ON THE DIET COMPOSITION OF PREDATORS USING FATTY ACID SIGNATURES: AN APPLICATION OF BAYESIAN INFERENCE ON LINEAR MIXING MODELS

Abstract

Determining the diet composition of predators is an important ingredient in many areas of ecology: understanding predator prey relationships, foraging behaviour of predators and consumption models to name a few. Iverson et al. (2004) developed a method based on the fatty acid signatures known as quantitative fatty acid signature analysis (QFASA). Fatty acids are the basic building blocks of most lipids and are indicative of diet, in the sense that higher level predators have limited ability to modify the fatty acids they ingest. Billheimer (2001) introduced a Bayesian compositional receptor model, where he apportioned the air pollution recorded a receptor site in Juneau Alaska into two components, woodstove smoke and automobile emissions. Building on this model we add components to allow for predator biosynthesis and differential fat content and also introduce a model which allows for design effects. Additionally we give some interesting results on the multi–modality of the logistic normal distribution. We also generalize the test of stationarity proposed by Priestley and Subba Rao (1969), based on evolutionary spectral ideas, as an alternative way of assessing when a MCMC sampler has reached its stationary distribution. xiv